Fluctuational transitions in periodically-driven nonlinear oscillators

Fluctuational transitions between the stationary states of periodically-dri ven nonlinear oscillators are investigated by means of numerical simulation s and analogue experiments for over-damped, weakly damped and chaotic motio n. It is shown that transitions take place along distinct most probable esc ape paths (MPEPs) in all three cases. The transition probabilities are comp ared with predictions based on the theory of the logarithmic susceptibility , (LS). It is found that, in agreement with theoretical predictions, the lo g of the transition probability displays an exponentially sharp dependence on the field frequency for the case of over-damped motion, and resonant beh aviour in the case of weak damping, and that it is linear in the field ampl itude in both cases. Particular attention is paid to the analysis of noise- induced escape from the quasi-attractor of a periodically-driven underdampe d oscillator: it is demonstrated that analysis of the escape process can be reduced to the analysis of transitions between a few saddle limit cycles o f low period, thus raising the possibility of an analytic description based on an extension of the LS theory.